Question

25. Air Conditioning While shopping for an air conditioner, Adam Bryer consulted the following table, which gives machine's BTUS and the square footage (ft") that it would col a ft (x) BTUS (y) 5000 150 5500 175 6000 215 6500 250 7000 280 310 7500 350 8000 370 8500 420 9000 450 9500 (a) Find the equation for the least squares line for the data. (b) To check the fit of the data to the line, use the results from part (a) to find the BTUS required to cool a room of 150 ft, 280 ft2, and 420 fť. How well do the actual data agree with the predicted values? (c) Suppose Adam's room measures 230 ft, Use the results from part (a) to decide how many BTUS it requires. If air conditioners are available only with the BTU choices in the table, which would Adam choose? (d) Why do you think the table gives ft instead of ft?, which would give the volume of the room?

Answer 1

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As for giuen dati- to Calaulak cEfftient relbhia and Euatio tor least uae? (ine, ue need to find Xy, y XY Xy xy 150 5000 750, cco aa,sco, a5, 000,000 175 5500 215 6000 1/a90, co0 4678 5, 36/c0o 000 50 6500 ,625000 63150o a50 CoO 280 1000 960 OC07E y00 3107500 ,395,000 96, l00 565000 FO0 30,625 30,250, 00D 49000 C00 500 64co cOo 1600 1000 3508000 3706500 3,I45,000 36, 900 7,50,Co 0 9000 3ıF&0000 (4b,400 S1006,c00 450 9500 5000 a2500 90, 350/000 29707,500aa,913,500 974,650546, 350,000 A)fo detymie E for atlae line we need to Knom'andb n (ExyEy)_ lo (2,912,5co-C X (,500 10 C97Y 650)-D970 n(Ear)-CEX ニ> 4-9099u806う14.9 Simiazly b EX)7500-/4.9x Ca97o 三y- m( - ど= mx tb Cs Scanned with CamScanner

b) Le 150 y-I4.9 -t asao 4.9 CI50+¥?0 5060 CAS Compared to aatal Sco0 Now tet - Q&o y- .92 P20 990 CAS Comfad to Acteal oco l4.9 0280+8a0 NO W let L- 420 Y=14.9 + O820 -> 14. 9C426)2820 9co CAS Compare d to actas 9000 Cte 330 Now we need to find y 26850 6250 Q 650 tien Gdam c need to BTU Qir Conditioner (d)ttalt ves fer ingtad-3 becaue Efcena Coafacity f a0 aix Condietfoner T> rot measered by te valeme accupies bu meafur& by tlp tOlal areq Heoom Coverd by H Condtioned air (c in tte Yoon thank you cs Scanned with CamScanner

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